Problem: Rewrite as a simplified fraction. ${3.68\overline{2} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3682.2222...\\ 100x &= 368.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3314}$ ${x = \dfrac{3314}{900}} $ ${x = \dfrac{1657}{450}} \text{or} {3 \dfrac{307}{450}}$